The Welfare Cost of InflationJOHN A. TATOM

I ii~PNE of the most controversial and least understoodconcepts of economic theory is that of the “welfarecost” associated with fully anticipated inflation. Othercosts or burdens of inflation receive considerableattention in the press, hut the burdens usimally dis-cussed are those associated with unanticipated infla-tion. Moreover, most of time costs of inflation whichare widely recognized and discussed involve transfersof income and wealtim from osme group to another. Forsociety as a whole, the value of these losses, or coststo some, tend to be offset by the value of gains, orbenefits, accruing to others. In contrast, little or noattention is focimsed on the net loss of valuable serv-ices whiclm society hears due to immfiatiomm, or whateconomists call the welfare cost of inflation.

It is widely agreed that most of the costs of inflationcan be eliminated by the creation of amm environmentwhere the inflation rate is stable or reasommably con-stant and the rate is correctly anticipated by partiesto financial contracts. Indeed, it has been suggestedthat not only can the costs of inflation he eliminated,but some benefits of inflation may he preserved orenhanced by promoting a stable anticipated positiverate. This argument has been put forward by rrianyanalysts, especially by a group of economic develop-ment economists of the “stnmctural” schookm More re-

~The !caclismg propssnent of this school is generally s’egarded tobe Bass1 Prehisch. A discssssion of the inflation theory of thisschool tnay be found in Dudley Seers, “A Theory of Infla-tion and Growth in Under-developed Economies Based on theExperiessce of Latiss America,” Oxford Economic Papers(June 1962), pp. 173-95; or Julio H. C. Ohvera, “OnSts’uctural Inflation and Latin-American ‘Structurahsnm’,”Oxford Ecotsomic Papers (Noveusber 1964), pp. 321-32.

cently, such an argument has been developed bymonetary economists in this country. Time implicationof such arguments is that a stabilization policy whichensures that existing inflation is fully and correctlyanticipated is, at worst, a satisfactory substitute for apolicy to eliminate inflation and at best, superior tothe elimination of inflation.

An orthodox analysis of inflation suggests that thereis a trade-off involved in anticipated inflation. Ac-cording to this analysis, there is a revenue resultingfrom inflation which accrues to a government whichcontrols the production of fiat money. This revenueprovides greater purchasismg power to the government,allowing it to increase government expenditures, or toreduce alternative sources of purchasing power, thatis, other taxes. Moreover, when the rate of inflation iscorrectly anticipated, the capricious effects of infla-lion on the distribution of income and wealth do notoccur.

But there is an “excess burden” of inflation, even ifit is correctly anticipated. That is, a given rate ofanticipated inflation will cost members of society moretiman the revenue which accrues to the government.The excess is called the excess burden, or “welfarecost” of inflation. Both the revenue and the welfarecost of inflation are positively related to the level ofthe rate of inflation. Therefore, the “best” rate of in-flation must be chosen with reference to the revenue-cost trade-off of inflation and the revenue potentialand associated costs of alternative revenue sources.

The case supporting a stable perfectly anticipatedpositive rate of inflation is sfrengthened by argunments

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which assert that the welfare cost of inflation is vem-ysmall. In some of these arguments, the size of thewelfare cost of inflation is absolutely dismissed. Anotable example is the Presidential Address of Pro-

fessor James Tobin to the American Economics Asso-ciation in December 1971. Discussing the relationshipbetween unesnployment and inflation, he said of thecost of inflation:

Accordismg to ecosmomic theory, the tsltimate socialcost of almticipated ismflatiosm is time wasteful use ofresources to ecommomize holclismgs of currency andotlmer noninterest—bearismg means of pavmemmt. I sus-pect that intelligent laynmen would be utterly as-tounded if they realized that this is the great evilecosmomists are talkismg about. ‘P1mev Imave imagismed amuch more devastating cataclysnm, with Vesimviusvengeftsliy punishing the sinsmers below. Extra tripsbetween savings banks and comsmmercial hasmks? Whatamm anti—climax 2

Other important examples may be found in the litera-hire on public finance. One of the best treatments ofthe welfare cost of taxatiosm is that of Richard A. andPeggy B. Musgrave in their hook, Public Finance inTheory and Practice. However, their work containsno discussion of the welfare cost of anticipated infla-tion. Moreover, they do emphasize the revenue frominflation.m

This article is intended to serve two purposes. Thefirst ptsrpose is to explain the welfare cost of antici-pated inflation. it is shown that this cost is not negli-gible. Thus, it is smot a matter of indifferesmce whethera government follows a policy of pursuing a veryhigh or a very low rate of fully anticipated inflation.The second purpose is to show that, on the groundsof efficient taxation alone, the optimal rate of antici-pated inflation and its revenue potential are not large.On rather generous assumptions favoring inflationaryfinance, it is demonstrated that tax efficiency does

not justify a positive rate of inflation,

The concern here is the cost associated with a con-stant ammd correctly anticipated inflation rate. Thecosts of ummanticipated immflation wlmich imnpact on par-ties to trammsactions imm credit or resource markets, fixedincome recipients, and taxpayers ism general are ig-

2jassmes ‘I’ssbiss, Inliatioms asmd Unesmmployment,” flsc AmericanEconomic Review (March 1972). p. 15.

:sllichard A. Msssgrave and Peggy B. Musgrave, Public Financein Theorp and Practice ( New York: McCraw—Hill BookCossspany, 1973), p. 526 in footsmote 11, they dismiss thesmotiosm of a welfare cost of inflatioss by arguing that, aspresented by some theorists recently, it is ‘a rather quaintbasis osm which to assess the case against inflation.”

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NOVEMBER 1976

nored.4 These costs are substantial; indeed, theydwarf the cost addressed here. Nonetheless, it istheoretically conceivable that these costs may beavoided in an inflationary esmvironment if inflation iscorrectly anticipated.

The seminal article on the welfare cost of inflationis Martin J. Bailey’s 1956 article “The Welfare Cost ofInflationary Finance.”5 He examined the cost of per-fectly anticipated inflation to holders of real moneybalances in a stationary economy and illustrated thosecosts using data from several famous hyperinflationsin various countries. Bailey also identified the revenuefrom inflationary money creation which accrues to agovernnment which produces fiat money. This revenueis a transfer from money owners to all householdsthrough the government. Therefore, he argued thatthe social cost or excess burden of an inflation tax isthe total cost to money o\vners le.ss the transfer togovernment. Bailey’s analysis is almost identical tothe analysis of the welfare cost of an excise tax.6

A considerable literature has developed followingBailey’s cost analysis. The focus of this literature hasbeen on the implications of analyses such as Bailey’sfor an “optimum” rate of money growth and inflation.The prinmamy extensions of Bailey’s work have beenaccounting for growth of real output and for sometechnical considerations such as measurement, differ-ent expectation formation processes and the stabilityof an inflationary economy. Here we are interested inan exposition of the analysis of the cost of inflationand so a rigorous treatment of the development of the

The csssts of smnassticipated isiflatiosm are treated in smmost ismtro—ductory textbooks. Asm exceilesmt asmd brief discisssion smmay alsobe fomssmd ism J. Iluston McCulloch, Money and lssflatiosm:AMorsetarist A;sps’oach (New York: Academic Press, 1975). Seealso 1-lasms Il. Helhling and James E. Tmsrley, ‘‘A Prinmer onlnllatiosm : Its Conception, Its Costs, Its Cosmsequesmces,” thisReview (Jansmas 1975), pp. 2-8; Albest Ii. Burger, “TheEffects of Inflatiosi (1960-68),” this Review (November 1969),pp. 25-36; Michael R. Darhy “l’he Financial and Tax Effectsof Mosmetas Policy on’ Ismterest Rates,” Economic Inquiry(June 1975), pp. 271-73; and Jai-Hoon Yang, “The Case Foramid Against Issde.xatis,ss: Asm Attesmspt at Perspective,” thisReview (October 1974), pp. 2-11.

tmMartiss J. Bailey, “Time Welfare Cost of Inflationary Finance,”

The Jous’rsa/ of Political Econonty (Aps’il 1956), pp. 93-110.

“See the seseen ismsert, “The Welfare Cost of An Excise Tax.”‘rhe methodology asmd theory underlying the concept of awelfare cost and its ssmeassmrcnment here ammd in the discussionof time excise tax follow Anmrsld C. llarberger, ‘‘Three BasicPostsslates for Applied Welfare Econonmics: Ass ImmterpretiveEssay,”’l’hc Journal of Economic Literats,re (September1971), pp. 785—97; and Juimsm C. Hassse, “TIme Theory ofWelfare Cost Measuresssesst,” Journal of Political Economy(Decenmher 1975), pp. 1145-82.

FEDERAL RESERVE BANK OF ST. LOUIS NOVEMBER 1976

literature is not pursued. Instead an attempt is madeto present a “state of the arts” analysis drawing gener-ously upon this literature.

Suppose that the economy is initially in equilibriumand there is no inflation. The purchasing power of thestock of money is exactly that which households de-mand. This situation is represented in Figure I. Thedemand for real money balances, a nominal stock ofmoney deflated by the price level, is represented byD. The demand for real money balances is deter-mined by the level of real income, real wealth, andthe cost of holding real or financial assets.7 In FigureI, the demand for real money balances is shown to beinversely related to the level of market interest ratesrepresented by “the” interest rate, i. Other factorsaffecting the demand for money are held constantalong D. The supply of real money balances is thedollar value of the existing stock of money (M) de-flated by the general level of prices of goods andservices, the equilibriunm price level (Po). The exist-ing stock of money is assumed to have been producedby a central bank acting as an agent of the govern-mnent. No interest is paid on money in this analysis.The quantity of money can be changed throughcentral bank purchases and sales of financial assets, inpamticular, by buying and selling governnment bonds.It is assumed below that each government bond hasa principal anmount equal to one dollar and pays thenominal rate of interest i. Given the initial leveLs ofthe other determinants of the demand for money, theequilibrium level of the rate of interest is i’. Sincethere is no expected inflation initially, this rate ofinterest will be the same as the real rate of return (r)on capital, or real assets.

The price level depends on all factors determiningthe demand and supply of goods and services. In astationary economy the price level depends primarilyon the quantity of money.5 With unchanged prefer-ences of all spending units, the general level of priceswill be steady, if the quantity of money is constant.The actual rate of inflation will be the rate necessaryto ismsure that real balances and the level of otherreal variables are equal to their equilibrium levels.

If the nominal stock of money grows at rate p in-stead of zero, money holders will attempt to spend the

7Amm excellent discussiosm of the deniaimd for nsoney may befound is, Milton Friedman, “The Quantity Theory of Money— A Restatement,” iss Studies in the Quantity Theory ofMoney (Chicago: l’he University ssf Chicago Press, 1956).pp. 3-21.

~k statiomsary econosmsy is characterized by ass absence ofgrowth of resources or aggregate real income.

Figure

The Demand for and Supply ofReal Money Balances

One)’Ba lances

excess cash on goods and other assets in order tomaintain the purchasing power of their initial moneybalances. Because of the increased demand for goodsand assets, all dollar prices begin rising. The pricelevel will rise at rate p to eliminate a continuing ex-cess supply of cash and excess demand for goods andother assets. After adjustment to the increase in therate of monetary expansion from zero to p, the actualand anticipated rate of inflation, it, will equal p.

Inflation is a tax on real money balances because itraises the cost of holding a constant dollar of purchas-ing power. Since the nominal rate of interest rises tocompensate lenders for the erosion of wealth whichinflation would otherwise cause, the cost of holding areal dollar rises. An alternative way of viewing thiscost is that owners of mommey must increase their hold-ings of dollars at the same rate as inflation in order tomaintain the purchasing power of their cash balances.For each dollar held, the anticipated rate of inflationrepresents a cost of maintaining the purchasing powerof the dollar, in addition to the real return whichcould have been earned on real assets.

The effects of a positive rate of monetary expansionand actual and expected inflation at rate it can beseen in Figure II. The initial equilibrium, in the

Interest

S

io

0

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Figure II

The Demand for and Supply ofReal Money Balances with Inflation at Rate’T

B

mu0

Real MoneyBalances

IM/PI

absence of inflation, is indicated at point 1. The an-ticipation of inflation at rate it will raise the cost ofholding real balances to (rn + it), given the real rateof interest. Households will reduce their demand forreal money balances to m1, substituting other goodsand assets for the relatively more expensive servicesof money. Given the other determinants of the de-mand for money, equilibrium is restored at point 2.The growth in the nominal money supply will bematched by the rate of inflation so as to maintain thepurchasing power of money balances at the levelindicated by m,.

The total cost of perfectly anticipated inflation toowners of money is indicated in Figure II by the area(A + B + C). Area A is the increased cost of holdingm, units of real money balances. Money holders paya cost of ~mper period per dollar of real cash balances,instead of io. This additional cost is a maintenancecost. It measures the real value of goods and servicesforegone to add nominal money balances at rate it.

The total maintenance cost is this cost per unit of realmoney balances, it, times the level of real money bal-ances, m5.

The second component of the total cost, the areaB + C, is the real value of the services of moneywhich is given up by money owners due to inflation.The demand price, i, at each level of real balancesindicates the value of a unit of real balances per period.

For each unit of real balances given up by moneyowners, the value of the foregone services is measuredby the corresponding interest rate along the demandcurve.

The revenue from the tax on real money balancesaccrues to the government through the central bank.The revenue is reflected in the higher interest pay-ments on the growing amount of bonds held by thecentral bank. This revenue is the area A in Figure lI-

The revenue per period to the central bank isequivalently the real value of the continuous increase

in its nominal money output (~~ Since the rate

of monetary expansion ( = p) equals the rate

of inflation (it), the revenue per period (~¶~)is

equal to the level of real money balances times theM

rate of mnflation (-p- p = mm it). The added revenue ofthe central bank accrues to all households through thegovernment so the area A is not a net cost. Instead, it

is a transfer from money holders to all households.Therefore, the net cost to all households is the area(B + C).

Area (B + C) is the excess of the costs to moneyholders over the benefits of inflation at rate it. It is theexcess burden or welfare cost of inflation. Bailey andothers have illustrated this cost. During periods of in-flation (especially hyperinflation), payments proce-dures and habits change to avoid the capital losseswhich inflation imposes upon cash holdingY

However, it should be noted that the efforts toeconomize on money balances cited as illustrations ofthe excess burden of inflation are not necessary to theanalysis which identifies area (B + C) as the welfarecost. The identification of area (B +C) as the wel-fare cost implicitly assumes that the adjustment toperfectly anticipated inflation requires no use of re-sources. The adjustment has no direct cost, in thesense that scarce resources are diverted from the pro-duction of other real goods and services in order toeconomize on money holdings. Changes in the pay-

InterestRote

= rØ-FttN ‘3

A

S

Nu u

“See Bailey, “The Welfare Cost,” pp. 96-102. More detaileddescriptions of t~echanges in the payments process dmsrim,granipant and expected inflation have been written by FrankD. Graham, Exchange, Prices, And Production In Hyper-Inflation: Germany, 1920-1923 (New York: Russell & Rmsssell,1930); and Constarstino Bresciani-Turroni, The Economics ofInflation (London: C. Allen & Unwin, Ltd., 1937).

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FEDERAL RESERVE BANK OF ST. LOUIS NOVEMBER 1976

ments process and habits are costless in Bailey’sanalysis.

The area (B + C) is a measure of the lost value ofthe services of real money balances per period to allhouseholds. If the attempt to economize on realmoney balances due to inflation uses resources, theoutput of final goods and services available to house-holds will be reduced and there will be additionaldeadweight losses to society. These additional adjust-ments are associated with the recession or depressionwhich many believe must accompany continuous in-flation, even a prolonged steady rate inflation, andwhich have been observed with prolonged periods ofhyperinflation.m°

The size of the welfare cost of inflation, area(B + C) is the area of a triangle (C) and a rectangle(B). The area of the triangle is one-half the base, thereduction in real balances, times the height, the actualand expected rate of inflation. The area of B is thesame base times the height, the real rate of interest.Using the concept of elasticity, a general measure ofthe welfare cost may be written as:

(1) W/. C.e~(~’) it (it/2+r)

where e° is the elasticity of demand for real moneybalances with respect to the nominal interest rate,given the real rate of interest ro.m1 The welfare costof inflation is directly proportional to the elasticity ofdemand and the level of real money balances whichwould prevail in the absence of inflation or deflation.The welfare cost of inflation is inversely related to thereal rate of return on capital in an economy. Thewelfare cost increases at an increasing rate with theinflation rate.

A rough estimate of the size of the welfare cost ofinflation can be made using existing empirical re-search on the demand for money. Most estimates ofthe interest rate elasticity of demand for money (de-fined positively) indicate that it is about .15. That is,

10Since thi

5article concerns the cost of a sustained and cor-

rectly anticipated “pure” inflation, such arguments are out-side the scope of the analysis here and will he ignored.

liThe elasticity may be written symbolically as (— .

a one percent rise in the interest rate (for example,from 5 percent to 5.05 percent) will result in a .15percent reduction in the demand for money.12

The level of real money balances (measured incurrent prices) which would exist in the absence ofinflation, and the level of the real rate of return tocapital are more difficult to determine. A level of 5percent for the real rate of return is, if anything, ahigh estimate. An alternative estimate which is illus-trative is a 2 percent real rate.13 The U. S. moneysupply is about $300 billion. Most observers believethat the rate of inflation to he expected, in the nearterm, is about 5 percent.

Other things being equal, the percentage increasein the nominal rate of interest due to a 5 percent ex-pected rate of inflation as compared to no inflation is100 percent if the real rate is 5 percent, and 250 per-cent if the real rate is 2 percent. For a real rate of 5percent, one could expect m” to be 15 percent(.15 x 100 percent) higher than the present level, orabout $345 billion. Alternatively, a 2 percent real rateinmplies a level of real balances 37.5 percent largerthan at present, or $412.5 billion.

These estimates imply a range of the welfare cost ofinflation in equation (1) of $( 52 it + 517 it

2) billion

to $(62 it + 1547 it2) billion. For an expected rate of

inflation of 10 percent per year, the welfare costwould be $10 to $22 billion per year measured incurrent dollars. Alternatively, a 5 percent rate ofanticipated inflation involves a welfare cost of $4 bil-lion to $7 billion per year. These estimates give arough measure of the order of magnitude of the wel-fare cost of inflation.

Welfare costs of various parts of the U. S. tax sys-tem have been estimated. To provide some compari-sons, a few of the early esthnates are cited here.While the state of the art in some areas is crude, theseestimates provide useful approximations of the order

tm2See the survey of a literature by David F. W. Laidler,TIse Demand for Money: Theories and Evidence (Scranton,Pennsylvania: International Textbook Company, 1969),Chapter 8. To the extent that .15 is too low, the welfare costestisnates given below understate the welfare cost of infla-tion. Miltosm Friedman has srsggested that the .15 estimate‘nay be too low. See Milton Friedman, The OptimumQuantity of Money and Other Essays (Chicago: AldinePublishing Conspany, 1969), p. 143.

1~Milton Friedman, “Government Reventse frosn Inflation,”Journal of Political Economy (July/Augmsst 1971), p. 852and p. 854, has suggested that a real rate of interest aboutequal to the rate of growth of real per capita income has“some basis in experience and theory.” This s-ate of growthfor the United States is about 2 percent.

Page 13I so that e° (~-) is the reduction in real money balances per

msrsit increase in the expected rate of inflation. The totalredisetinn in real balances is this amount times the level ofthe expected rate of inflation.

FEDERAL RESERVE BANK OF ST. LOUIS NOVEMBER 1976

THE WELFARE

The analysis of the welfare cost of a tax is part ofthe overall theory of the effect of taxation. Most aim—alvsts of the cost of inflation argue by analogy thatinflatiosm is a tax on the purchasing power of money orreal cash balances, To rmderstand inflation asa tax itis necessary to review the analysis of the effect oftaxatiosm of another good, such as an excise tax ontobacco, alcohol, or long—distance phone calls.

In the accompasmving Figure, the demand (D) for aproduct X is showsm. The demand for X depends upossthe price of the product. Of course, the demarsd de-pends on other charactes-istics of the ecosmomic en-vironinent of all potential pssrchasers of product X.TIme most importasmt of these other determinants arethe prices of closely related goods stsclm as complementor substitute goods, the preferences of households, thereal income of households, and its distribution. Theseother factors are assumed to be fixed in time Figure.Suppose that product X, in the ahsesmce of a tax, canhe produced and sold at a current cost of $1/unit ofX, given technology and the value of resources Imeces—sarv to produce a ummit of X. This is indicated by thesupply curve in the Figure labeled S. In the absenceof a tax, competition among producers insures that thenmarket price will he $ i/unit assd the aniossnt pur-chased and srsld will he the amount households de—inand. for example, I millioss units ism the Figure.

Now suppose the government levies a tax on productX of $1/unit or 100 percent. The cost of producing andselliimg the product will rise to include tise cost of thetax. The market price svill rise to SZ/unit of X. House-holds will not cositimse to buy as much of the product.Instead, they will substitute, buyismg other goods whichhave not changed in price. lim the Figure, the demandfor X falls to .8 million units per period of tune.

The bw’den. or cost, of the tax to households is com-posed of three parts. First, households pay more forthe units the)- continue to buy. Second, householdsforego the benefits of consuming the tsnits which theyno longer purchase each period (200,000). The demandprice at a given quantity indicates the value of aunit of X to households. Therefore, consumers lose avalue of X indicated by the area under the demandcurve from .8 million units to 1 million units. Finally,households gain the benefits of more of other productsas resources move from the production of X to the pro-

The Effect of an Excise Taxon the Price and Output of Product X

duction of these other goods. The supply price in-dicated by curve S measures tIme cost of resotsrcesneeded to produce a unit of X. That cost is the maxi-mum valise of these resources in producing other goodsfor households, Tlmerefore, the value of the additionalother goods which households obtain is the area underS from 1 million units of X to .8 million units of X.1

The cost of the tax to households, in this example,is $900,000. The first component, the additional cost ofthe units households continue to purchase, is $800,000.This is the area of rectangle A in the Figure. The sec-ond part of the cost, the value of X which householdslose is $300,000. This is the area of the rectangle B($200,000) and the triangle C ($100,000). The tlmirdpart of the cost, the gain in the value of alternativeproducts is the area of the rectangle B (—$200,000).

tmIn the case of fiat money the third aspect here is absent. Noresources are free to move into the production of othergoods.

Price Per UnitofP’ ‘cix

$2

$5

5’

co~

uontity of XEli on ii

per Tine Period

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F AN EXCISE TAX

The second and third part of the cost can be com-bined to obtain the net cost to households of the shiftin the allocation of resources. This cost is $100,000 inthe example, the area of triangle C. Jt measures thecost to households of the distortion of their consump-tion patterns resulting from the tax. Society can pro-duce 1 million units of X and less of other goods or.8 million units of X and more of other goods. In theabsence of the tax, consumers would prefer the outputmix with 1 mullioim units of X to that with .8 millionunits. The value of the prefered mix over its alterna-live is the $100,000 measured by triangle C. The totalcost to purchasers of X may be stated as the sum ofareas A and C, It includes the yahie of product whichhouseholds must forego to pay the tax (A) and the netvalue of the product X which households forego due tothe tax.

The proceeds or revenue from the tax is the tax/unittimes the number of units which households continueto buy. In time example, this is the area of rectangle A.The proceeds of the tax are not tnily a cost to house-holds, In fact, time proceeds will be spent on goods ortransferred back to households. The tax reveimue doesnot affect the capacity of the economy to producegoods and services. The value of the foregone productfor households, measured by rectangle A, is the value ofthe product which government either purchases for allhouseholds or permits households to continue to pur-chase through a transfer of the tax revenue back tothem. Rectangle A is not a cost to society. It is merelya financial transfer within the economy. Area C, thetriangle, is the only remaining cost of the excise tax.

The analysis of the cost and benefits of a tax maybe summarized as follows. The tax imposes costs onhousehold purchases of the taxed good. The cost ismeastsred by areas such as (A+C). The governmentreceives proceeds of the tax equal to an area such as A.This benefit of the tax accrues to all or some membersof society. The cost of the tax exceeds the benefit ofthe tax by an area such as C. The excess is called an“excess burden” or the “welfare cost” of the tax on X.It measures the net loss to all households due to thedistortion of resource allocation caused by the inter-ference in the market for product X. In the example,the welfare cost is $100,000 per period.

A general measure of the welfare cost of an excisetax may be developed from the concept of the price

elasticity of denmand. This elasticity is a measure ofthe responsiveness of the quantity of a product whichhouseholds demand, to changes in the price of theproduct. It may be defined as:

1 -~ percentage change in quantity of X demandede — percentage change in the price of X

The elasticity measures the percentage reduction inthe quantity which households demand for each onepercent rise in the price of product X.

The size of the welfare cost, approximately the areaof a triangle such as C, is one-half the product of thesize of the reduction in demand and the size of theincrease in price. The size of the reduction in demandis related to the rise in price through the elasticity ofdemand. The welfare cost of a tax can be written as:

(2) W.C.zzr½e(P0L)t2

is the percentage rate of the tax, the tax/unitby the original price.’ In the example, the

of demand is .2, the total expenditure on(P0X0) is olme million dollars per year, and100%. Thus, the welfare cost is $100,000 per

In equation (2), the welfare cost of a tax is shownto be an increasing function of the elasticity of de-mand, The welfare cost of a tax increases with thesquare of the tax level, and is proportional to the sizeof the original tax base.

Equation (2) is not the most general measure ofthe welfare cost of a tax, There are other considera-lions, such as file level of existing taxes on other goodsand services and the technical or market conditionsdeternmining supply, which affect the measurement ofwelfare cost, However, the treatnment of this simplecase is sufficiently general for the discussion of moneyand inflation,

2Siinilar equations may be found in Arnold C. Harberger,“Taxation, Resource Allocation, and Welfare,” Taxation andWelfare (Boston: Little, Brown and Conmpany, 1974), p.34; and Richard A. Musgrave and Peggy B. Musgrave,Public Finance in Theory and Practice (New York: Mc-Graw-Hill Book Company, 1973), p. 456.

wheredividedelasticitythe goodthe tax isperiod.

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FEDERAL RESERVE BANK OF ST. LOUIS NOVEMBER 1976

of magnitude of the costs. The major tax in theUnited States is the personal income tax. It distortsthe choice between labor and leisure, encouraginglonger vacations, greater absenteeism, early retire-ment and other means of reduced effort. The welfarecost of this tax has been estimated for 1961 to he onebillion dollars per year. If the welfare cost per dollarof revenue were the same in 1975 as in 1961, the wel-fare cost in 1975 would be about $3 billion. Account-ing for the substantial increases in the marginal taxrate since 1961 would dramatically raise this esti-mate.tm4 Musgrave and Musgrave have placed theorder of magnitude of the welfare cost of selectivesales and excise taxes at $3 to $4 billion per yearfor 1970 and that of the corporate income tax atabout $1 billion per year.15 The welfare cost of fivepercent anticipated inflation exceeds the welfare costof the corporate income tax and it may be as large asthat of the personal income tax.

There are two problems with the cost measureswhich must be pointed out. First, they rely on anestimate of the elasticity of demand for money withrespect to the anticipated inflation rate ~vhich may bea serious underestimate of that elasticity.16 Second,the measure in equation (1) is for an economy withzero growth of real output, not for a growing economysuch as the United States.

The relevant elasticity of demand for money is theelasticity of demand with respect to the anticipatedrate of inflation. This elasticity will osmly be related tothe interest rate elasticity if, during the period whenthe interest elasticity is estimated, movements of theinterest rate reflect only changes in inflation expec-tations and not changes in the real rate of return oncapital. There is a substantial volume of literaturewhich argues that the demand for money is not verysensitive to changes in real rates of return on capital,while it is sensitive to changes in the anticipated rateof inflation. A given change in market interest rateswhich reflects a change in inflation expectations

m4see Arnold C. Harberger, “Taxation, Resource Allocation,and Welfare,” Taxation and Welfare (Boston: Little, Brownand Company, 1974), p. 47.

55See Musgrave and Musgrave, Public Finance, pp. 458-59.

16

Robert Barro implicitly uses an estimate of this elasticity ofone half. Accordingly, his estimate implies a welfare cost ofinflation more than three times the size given here. SeeRobert J. Barro, “Inflationas’y Finance and the Welfare Costof Inflation,” Journal of Political Economy (September/October 1972), pp. 978-1001.

should have a sizeable impact on the demand formoney vis-a-vis the demand for real and other finan-cial assets. On the other hand, a given change in themarket rate due to fluctuations in the real rate ofreturn on capital will affect household consumption-saving choices with little impact on the compositionof desired asset portfolios, in particular, the demandfor money. To the extent that observed interest ratechanges have been due to changes in the real rate,the estimate of the interest elasticity understates theelasticity of demand for real money balances withrespect to the expected rate of inflation.mT Conse-quently, the true welfare cost measure would behigher than these estimates.

The second problem with the analysis above is thatit ignores the effect of economic growth on the wel-fare cost of inflation. It has been suggested that thewelfare cost of inflation is smaller in a growingsociety.18 If this suggestion is correct, the estlinate ofthe annual cost of perfectly anticipated inflation istoo large.

To assess the effect of growth on the wellare cost,consider Figure III. Growth increases the demand forreal money balances from D to D’. The process ofgrowth is continuous but it is sufficient to look at thediscrete shift from one period to the next. For thesame rate of anticipated inflation, ‘it, the percentageincrease in the quantity demanded of real balances isequal to the “income elasticity of demand” times therate of growth of income. Since the demand formoney at each point along D increases by the samepercentage, the demand at points 1 and 2 grows bythat percentage, in one period of time, to points 1’and 2’. The demand for real money balances at thesmaller level, 2, grows by a smaller absolute amountthan at the higher level 1. The base of the triangle C’and of rectangle B’ is larger than in C and B by thepercentage growth in demand. For the same rate of

‘~A classic discussion of the propositions concerning the de-inand for money may be found in Friedman, “The QuantityTheory,’ or “Interest Rates and the Demand for Money.”Both may be found in Friedman, Tlse Optimum Quantityas Chapter 2 and Chapter 7, respectively. An example of amore rigorous derivation for an inventory theoretic demandnsodel may he found in Edi Karni, “The Value of Time andthe Demand for Money,” Journal of Money, Credit andBanking (Fehrnasy 1974), pp. 45-64. Considerable confu-sion continues to exist over the difference between thesetwo elasticities. For an example, see Edmund S. Phelps,“Inflation in the Theory of Public Finance,” The SwedishJournal of Economics (March 1973), pp. 67-82, especiallyp. 76 and p. 82.

15See Charles D. Cathcart, “Monetary Dynamics, Growth,and the Efficiency of Inflationary Finance,” Journal ofMoney, Credit and Banking (May 1974), p. 189.

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FEDERAL RESERVE BANK or ST. LOUIS NOVEMBER 1976

Fig ore tO

Growth of Income and theWelfare Cost of Inflation at Rate ¶

money curve in Figure II. In the short-run the analy-sis of the welfare cost of inflation must either accountfor shifts in the demand curve or for other changeswhich are necessary to keep the demand curve in itsoriginal position. The latter method is pursued here.A policy of implementing a permanent rate of inflationis described below which obviates the shift in thedemand curve. This policy also clarifies the effect ofinflation on the government’s budget.

Given a level of nominal money balances, a changein anticipations to a higher rate of expected inflationwill reduce real money balances through a one-timechange in the general level of prices. The price levelmust be sufficiently higher to eliminate the excesssupply of real money balances. This is illustratedin Figure IV, Panel A. The reduction in real money

D balances demanded, from point 1 to point 2 willcreate an excess supply of real money balances, given

0 the initial price level, P0. The corresponding excessm

1mn

0nl

1Real Money demand for other real goods and services will result

Bolunces , .

in a one-time surge in prices to P1. This rise in thelevel of prices eliminates the excess supply of realcash balances at point 2.anticipated inflation, the annual welfare cost in-

creases through time in a growing economy. It growsat the rate of growth of the demand for money.1°Therefore, the estimates of the annual welfare cost ofanticipated inflation are again, understated, contraryto the position mentioned above.

The analysis of the welfare cost of perfectly an-ticipated inflation in the last section is based upon anassumption of long-run adjustment to the anticipation.The analysis compares two equilibrium situations suchas points 1 and 2 in Figure II. It ignores the adjust-ment process by svhich real money balances are re-duced and any short-run cost which may be associ-ated with the transition. This assumption appears tobe critical in light of the theoretical results arisingfrom the recent rediscovery of wealth effects oneconomic behavior. The anticipation of inflation willnot leave “other things equal” along the demand for

itt’j’he analysis here, following the empirical literature, assumesthat the interest rate and anticipated inflation rate elasticitiesof demand for money are unaffected by the level of otherdetenninants of demand such as the level of income.

It may be noted in Figure III that at the given rate ofinflation, it, the supply of real money balances, ml, grows atthe rate of growth of demand. Therefore, the equivalent ofarea A in Figure H also grows at this rate.

The analysis of the previous section has two implicitassumptions. The first is a technical point. The wel-fare cost analyzed there is not the cost associated withmoving along a price path such as P0AP in Figure V.Instead, the level of prices will surge upward whenthe rate of money growth rises from zero to p = ito.

Thus, the price path associated with the nominalmoney supply path M in Figure V will be POABP’,where time to is the point when the rate of moneygrowth rises.

The second implicit assumption is more serious. Theanalysis above ignores wealth effects. In particular,the surge in prices to level P1 will reduce the realvalue of net monetary assets in household portfolios.The analysis assumes that this short-run reduction inreal wealth has no effect on the demand for real cashbalances and other goods and services.

The initial reduction in real wealth due to a pricesurge will cause households to attempt to restore theirlost wealth. Thus, households reduce their spendingon goods and services and their desired holdings ofreal cash balances. Since part of the excess demandfor goods and seMces is eliminated due to the wealthreduction, the price surge will be smaller whenwealth effects are included. Also, the increased sav-ing rate of households to restore wealth will reducethe real rate of return on physical capital. Thus, the

interestRote

r r0

+TT

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FEDERAL RESERVE BANK OF ST. LOUIS NOVEMBER 1976

Figure IV

Anticipated Inflation (‘II),Wealth Effects, and the Price Level

(M9/P

1)

PANEL B

nominal rate will not increase by the rate of antici-pated inflation.

The ultimate effects on the analysis are shown inFigure IV, Panel B. The demand for real money bal-ances will shift to the left due to the smaller level ofwealth (W1) with price level P2. Also the nominalinterest rate will be higher and reflect the rate of

inflation Ito, but at interest rate i2 instead of ii. Thereal rate of interest is lower, r1, The earlier analysis iscomplicated by short-run changes in two of its param-eters: the decline in the real rate of interest, and thesmaller level of real wealth.

The cost of moving along a price path such asP0AP in Figure V, allowing for the short-run effects ofthe reduction in desired real balances, may be foundin a policy context which removes these analyticalcomplications. The reduction in desired cash balancescan be facilitated by a one-time accommodating mone-tary policy, rather than the one-time surge in the pricelevel. An open market sale of bonds in exchange forthe excess cash balances, (m0 — m1) in Panel B, willleave wealth unaffected.2° The real money supplyfalls to m1 via a decline in the nominal money supplyrather than a higher price level. Wealth, the pricelevel, and the real rate of interest will be unchanged.Since these are the major determinants of the demandfor money, other than the expected rate of inflation,there will be no shift in the demand for money. Theincrease in the rate of monetary growth requires anopen market sale of bonds initially to, in effect, “soakup” the excess real cash balances which it initiallycauses.2m Furthermore, to avoid a wealth effect in thefuture from the rising price level, net financial wealth,the money stock plus the value of debt held by thepublic, must grow at the same rate as prices.

The revenue from inflationary finance may also bemore clearly seen in such a conceptual framework.The open market sale of government bonds by thecentral bank increases the real value of governmentdebt held by the public. From the government’sviewpoint, the revenue effect of the inflation includesthe additional revenue of the central bank (it m1)less the real interest payment on the increase in publicdebt. Since the increase in the public debt equalsthe permanent desired reduction in real money bal-ances due to the inflation expectation, the revenueof inflation in Figure II is the area A less area B

(M/P) ft (m — m1

20The relevant real wealth variable includes real money bal-ances, the real value of government debt, and the real valueof capital.

2lThe effects of inflationary expectations on the price leveland real rate of interest have also been noted by Cathcart,“Monetary Dynamnics,” and Leonardo Auemheimer, “TheHonest Government’s Guide to the Revenue from the Crea-tion of Money,” Journal of Political Economy (May/June1974), pp. 598-606. Auernheimer also pointed out theimportance of the initial open market sales prior to a higherrate of monetary expansion to avoid the one-time pricesurge.

mr+’TT

iFro+lio

0

,r+’Tr

1110

(M0

/P1

(M0

/P0

)

PANEL A

i0Zr

0

OlWo)

m1

M0/P

2m

0

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FEDERAL RESERVE BANK OF ST. LOUIS NOVEMBER 1976

Figure V

The Money and Price Path:From Price Stability to Money Growth

and Expected Inflation at Rate~oNominal

Money Supply (M}Price Level (P)

Logarithmic Scole)

current dollars, or. with a 5 percent rate of expectedinflation, $15 billion. The area B in Figure II dependsupon the size of tile reduction in real money balancesdue to a 5 percent rate of inflation and upon the levelof the real rate of return on assets, tile nominal in-terest rate in the absence of inflation. Employing theearlier estimate of an elasticity of demand of .15, andeither of the two estimates of the real rate of interest(2 percent or 5 percent), the area of rectangle B is$2.25 billion. The area (A — B) for a 5 percent rateof inflation is $12.75 billion, in current dollars.22

The measure of revenue as the area A less area Bis subject to an additional important qualification. Notall of the money stock is provided through the mone-tary authority. In fact the stock of money suppliedby the monetary authority, the monetary base, is lessthan forty percent of the stock of money. The rela-tionship betsveen the monetary base and the moneysupply is remarkably stable, so the government’sshare of the total stock of money may be definedas (sm) where s is the ratio of the monetarv base tothe money supply.

to Time

The subtraction of area B from the revenue of in-flation also affects the earlier analysis of the cost ofinflation. Area B remains part of the real value oflost money services per period. In addition, it repre-sents the increase in the real value of interest pay-ments per period due to the larger public held debt.Therefore, the gross burden or total cost is (A ±C).

The analysis in the previous section is little affectedby dropping the long-run perspective. Both the reve-nue and the total burden of inflation are reduced bythe size of area B. The revenue (A) is reduced toaccount for the increased interest payments requiredon the larger public debt. The total burden (A ±B

+ C) is reduced because of the receipt by householdsof larger annual interest payments on the public debtrepresented by area B. Hence, the excess burden orwelfare cost remains the same, area (B ±C) in Fig-ure II.

The size of the revenue from inflation depends onthe elasticity of demand for real money balances withrespect to the expected rate of inflation. The area Ain Figure II is the rate of inflation times the level ofreal money balances, about $300 billion measured in

The base for government revenue from moneycreation is not the total money supply, but only themonetary base. Therefore, the revenue area (A — B)above must be multiplied by s to present an accurateestimate of the governmnent revenue from inflationaryfinance.23 With an estimate of s of 40 percent, thegovernment revenue from a 5 percent rate of inflationis approximately $5.1 billion (.4 x $12.75 billion).

In contrast, the Federal revenues in 1975~fromthe

corporate income tax and personal income tax were$42.6 billion and $125.7 billion, respectively. A rateof inflation of 5 percent appears to be a very costlymethod to raise a modest amount of Federal reve-nue. The welfare cost per dollar of revenue raisedfrom a monetary policy \vhich yields a 5 percentactual and expected rate of inflation, using the costand revenue figures above, is 80 to 120 cents perdollar of government income. The welfare costs perdollar of revenue from the personal income tax and

22J~~a growing economy, the annual revenue frcsm mcsneycreation is larger since even price stability requires that thesupply of nominal nsoney grow at the rate of growth ofcleusancl fcsr real money balances. This larger revenue growsat the rate of growth of money demand and the welfarecost. Sec footnote 19 above.

23The remainder of the revenue (A-B) accrues, through thebanking system, to hank (swuers and, through competition,to their depositors. The welfare cost analysis above is notaffected by- relaxing the assumption that all money is sup—plied by the monetary authority. The cost of holding banknioney rises in the same manner as it does for currency.

in

in M’ ~er~M

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FEDERAL RESERVE BANK OF ST. LOUIS NOVEMBER 1976

The relevant measure of cost for an efficient taxsystem is the marginal cost per dollar of additionalrevenue, not the average cost.24 An efficient taxsystem raises a given total revenue from varioustaxes with a minimum total cost. Therefore, for eachtax, the cost per dollar of revenue must be equatedat the margin. It is difficult to reach definitive con-clusions concerning the optimum rate of monetaryexpansion and inflation without knowledge of themarginal cost of alternative revenue sources. Unfor-tnnately, this cost for all alternative taxes has notbeen estimated. Nevertheless, an upper bound onthe size of such marginal costs has been placed at10 cents per dollar of government receipt and thismay be used here.25

The marginal welfare cost of inflationary financemay be written as:

e° 1 26

(2) c = (y~~) (~)Additional revenue is obtained from a higher rate

of inflation only when the interest elasticity is lessthan one; if the interest elasticity rises with the rateof inflation, maximum revenue from inflation occurswhen ea is equal to one. According to Equation (2),as e°approaches one, the marginal welfare cost ap-proaches infinity. Also, Equation (2) indicates thatthe marginal cost is greater, the greater is the rateof inflation or interest elasticity of demand for money,and the smualler is the government’s share of themoney supply. Therefore, the estimates of an interestelasticity of .15 and share, s, of 40 percent, yielddownward-biased estimates of the marginal welfarecost of government revenue from money expansion.

The marginal welfare cost in equation (2) is con-stant and equals 44 percent, given the estimatesabove. This level is well above the maximum estimateof the marginal well are cost of alternative revenuesabove. Therefore, efficiency of the tax system doesnot warrant inflation or inflationary finance. Addi-tional revenue, within the relevant range for theUnited States may be more cheaply obtained throughother sources of revenue, not through inflation.27

In recent years, some economists have argued thatthere are benefits to inflation and, if the rate is stableand can be fully anticipated, there is little or no costto society. The cost of perfectly anticipated inflationis its wellare cost. It results from the loss in welfaredue to the substitution away from real money bal-ances. While this cost may be small in relation to thecosts of redistributions of income and wealth wheninflation is unanticipated, it is comparable to the wel-fare costs of other major components of the U. S. taxsystem at levels of inflation as low as 5 percent.Moreover, the size of the welfare cost of inflationincreases rapidly with the size of the rate of inflationitself. The welfare cost of inflation is independent ofresource costs incurred to economize on cash bal-ances; indeed, the analysis assumes these costs to bezero. To the extent that valuable resources are usedto economize on cash holdings, the cost of perfectlyanticipated inflation is even greater.

One of the primary benefits of inflation is therevenue it produces for the government. It has beensuggested by some analysts that efficient taxationrequires taxing cash balances through inflation. In-deed, since the demand for money is relativelyinsensitive to changes in the cost of holding money,high rates of inflation, appear to some to be justifiedon tax efficiency grounds. It has been shown herethat tax efficiency can not justify a positive rate ofinflation, even employing strong assumptions favoringthe inflationist case.

The “tax efficiency argument” forces the questionof the optimal rate of inflation into the domain ofpublic finance. The answer depends upon the mar-

27A marginal welfare cost which is constant and above themnarginal cost of alternative revenue actually suggests anefficient polity of deflation with revenue losses for moneycreation being replaced by additional revenue from alterna-tive taxes. However, it may he expected that the interestelasticity of demand for money is an increasing function ofthe rate of inflation. Therefore, the marginal welfare cost ofrevenue from money creation will fall to the 10 percent levelat a small i-ate of deflation.

the corporate income tax in 1975 were on the orderof three cents per dollar of revenue.

2lThis point has been emphasized by Alvin C. Marty, “ANote on the Welfare Cost of Money Creation,” Journal ofAlonctary Economics (January 1976), pp. 121-24; and inEdward Tower, “More on the Welfare Cost of InflationaryFinance,” journal of Monetj, Credit and Banking (Novem-ber 1971), pp. 850-60; Cathcart, “Monetary Dynamics;”Phelps, “Inflation;” Barro, “Inflationary Finance.”

25See Tower, “More on the Welfare Cost,’ p. 856. The esti-mate of 10 percent is also consistent with the work ofEdgar K. Browning, “The Marginal Cost of Public Funds,”Journal of Political Economy (April 1976), p. 295. Heestiniates the marginal cost for the individual income tax,including administration and compliance costs, to be 9 per-cent in 1974.

2OThe derivation of this equation is found in the Appendixas equation (8), where ee above is the interest rate elas-ticity of demand for real money balances, given the realrate of interest.

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~AL RESERVE BANK OF ST. LOUIS NOVEMBER 1976

ginal costs of alternative revenue sources. While fur-ther research on the nature of other taxes is therebyrequired, the examination here supports some strongconclusions. Even if the marginal cost of alternativesources of revenue is much larger than the level sug-gested here as an upper bound, tax efficiency offersno support for inflationary public policy.

The efficiency of the tax system and the revenuepotential of inflation appear to be insignificant argu-ments in the debate over the “optimum” rate of infla-tion. Such arguments have considerable theoretical

appeal but, upon close examination, are of hale prac-tical importance. A positive rate of inflation is notsupported by these arguments. Furthermore, the ad-ditional revenue obtained from a rate of inflation ashigh as 5 percent is small relative to the revenueobtained through money creation with price stabilityor relative to the revenue from alternative taxes. Thepractical importance of the “tax efficiency argu-ment” is also limited by existing inefficiencies in thepresent tax system as well as the apparent difficultiesof maintaining a steady and fully anticipated rate ofinflation.

The Effielent Taxation of Money

A general derivation of the welfare cost, revenue, andmarginal cost of inflationary fimiance may be found whichis independent of the functional form of the demand forreal money balances. The revenue from money produc-tion is:

(1) B -~sin

where s is the ratio of the monetary base to money andis assumed to be constant. The effect on revenue of achange in the rate of inflation is:

am(2)— = s m (1+ —fl——).dir mu an

Let the demand for real money balances be writtenas a function of the expected rate of inflation, 0(11). Thewelfare cost of inflation is:

(3) \V J~~ (x) d x—i t(n) ±r Q (o)

The effect of an increase in the expected rate of inflationis:

ut is assumed here, as in the text, that the real rate of returnis unaffected by the expectation of inflation or that a onepercentage point rise in the expected rate of inflation addsone percentage point to the nomuinal interest rate.

The marginal cost of inflationary finance, c, is:

dW dW~rIB —~i~’(5) c= —-=—~—.—

dli dn dlfl (ni* i~’)5

The elasticity of demand for money with respect to thenominal rate of interest, given the real rate of interest,and with respect to the expected rate of inflation aredefined as:

am i am i(6) E~ ~ andai mu arm in in

— ani yr n()E =—— ~=—~ —

~ art Imi i-il,

Then the marginal cost, c, may be written alternativelyas:

(8’) ~=il!~tts(n-i Err) s(l-E~)

In the usual analysis of the welfare cost of inflation aspecial functional form is employed in which the elasti-city of demand for money with respect to the expectedrate of inflation is an increasing function of the expectedrate of inflation. In particular, it is written as:

(9) E~:~hn

where b is a constant. For this case, the earlier equationsbecome:

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FEDERAL RESERVE BANK OF ST. LOUIS NOVEMBER 1976

(2’) s in(l-i Nclii

dW(4~)———-= h mu’dii

—, div h i(ol c = -a—- = (I-i h)

Since the elasticity of demand for money increases withthe rate of inflation, the demand will become elastic withrespect to either the rate of inflation or the nominal inter-est rate at a sufficiently high rate of inflation. Therefore,there is a rate of inflation which maximizes revenue, ahigher rate of inflation yields lower revenue from moneyproduction. This maximum rate of inflation (max) may

be found by letting equal zero in equation (2’).

(10) rI flax = _~_— r0

b

The marginal cost in (5’) is infinite at tIns rate ofinflation.

The size of the revenue maximizing rate of inflationdepends upon the value of b and the real rate of interest,r°.The precise level of b for the United States is un-known, although some evidence exists on the appropriatenumber. A level of 2 is probably far too low and may serveas a lower bound. Estimates ranging up to 78 have beenmade for the U. S. Some illustrative values which havebeen cited are: 2, 10, and 20 years.2 Together with thealternative real rates of interest in the text, the revenuemuaximizing annual rate of inflation is found to vary from

2See Milton Friedman, “Government Revenue from Inflation,”Journal of Political Economy (July/Angmmst 1971), pp. 851-53.

zero to 48 percent with the mid-range, 5 to 8 percent,for b = 10. The rate of inflation warranted by an efficienttax system will be substantially less than the revenuemaximizing rate,

The marginal welfare cost of revenue from moneycreation is larger, according to equation (5’), the largeris b, the real rate of interest, or the expected rate of infla-tion. The marginal cost, c, is zero when the nominalinterest rate is zero, that is, when the expected rate ofdeflation equals the real rate of return on capital. Themarginal welfare cost of revenue with price stability maybe found from equation (5’) by letting the nominal rateequal the real rate of interest.

Using the levels of b above and the two levels of thereal rate of interest, 5 percent or 2 percent, the marginalwelfare cost ranges from 10 percent to infinity, forit = 0. In the smallest case (10 percent), the level of b is2 years, and r is 2 percent, i.e. the interest rate elasticityof demand (rb) is only .04, much less than the elasticitygenerally obsers’ed. Moreover, tlus minimum level of themarginal welfare cost with price stability is equal to themaximum estimate of the alternative marginal cost citedin the text. Therefore, under the most extreme assump-tions used here to support inflationary finance, efficienttaxation warrants price stability. Even if the alternativemarginal cost is doubled to 20 percent, the warrantedrate of inflation with these assumptions is only about1.5 percent. For more reasonable assumptions concerningb and r, efficient taxation would warrant deflation,

The “tax efficiency” argument may not be used tojustify high rates of inflation. In fact, this argument sug-gests that the warranted rate is negative, but less inmagnitude than the real rate of interest.

Page 22